What about a hypothetical country that is shaped like a donut, and the hole is filled with four small countries? One of the countries must have the color of one of its neighbors, no?
Comment on What are the most mindblowing fact in mathematics?
mookulator@lemmy.world 10 months ago
The four-color theorem is pretty cool.
You can take any map of anything and color it in using only four colors so that no adjacent “countries” are the same color. Often it can be done with three!
Maybe not the most mind blowing but it’s neat.
Blyfh@lemmy.world 10 months ago
Afrazzle@sh.itjust.works 10 months ago
I think the four small countries inside would each only have 2 neighbours. So you could take 2 that are diagonal and make them the same colour.
SgtAStrawberry@lemmy.world 10 months ago
Looks to be that way one of the examples given on the wiki page. It is still however an interesting theory, if four countries touching at a corner, are the diagonal countries neighbouring each other or not. It honestly feels like a question that will start a war somewhere at sometime, probably already has.
Vegasimov@reddthat.com 10 months ago
In graph theory there are vertices and edges, two shapes are adjacent if and only if they share an edge, vertices are not relevant to adjacency. As long as all countries subscribe to graph theory we should be safe
Blyfh@lemmy.world 10 months ago
But each small country has three neighbors! Two small ones, and always the big donut country. I attached a picture to my previous comment to make it more clear.
Pronell@lemmy.world 10 months ago
In your example the blue country could be yellow and that leaves the other yellow to be blue. Now no identical colors touch.
Afrazzle@sh.itjust.works 10 months ago
Whoops I should’ve been clearer I meant two neighbours within the donut. So the inside ones could be 2 or 3 colours and then the donut is one of the other 2 or the 1 remaining colour.
ikilledlaurapalmer@lemmy.world 10 months ago
BewilderedBeast@mander.xyz 10 months ago
Afrazzle@sh.itjust.works 10 months ago
BitSound@lemmy.world 10 months ago
In that image, you could color yellow into purple since it’s not touching purple. Then, you could color the red inner piece to yellow, and have no red in the inner pieces.
sanguinepar@lemmy.world 10 months ago
I read an interesting book about that once, will need to see if I can find the name of it.
L3s@lemmy.world [bot] 10 months ago
Artisian@lemmy.world 10 months ago
Note you’ll need the regions to be connected (or allow yourself to color things differently if they are the same ‘country’ but disconnected). I forget if this causes problems for any world map.
rycee@lemmy.world 10 months ago
I suspect that the Belgium-Netherlands border defies any mathematical description.
dandroid@dandroid.app 10 months ago
If you had a 3 dimensional map, would you need more colors to achieve the same results?
eran_morad@lemmy.world 10 months ago
this whole thread is the shit.
clumsyninza@lemmy.world 10 months ago
Isn’t the proof of this theorem like millions of pages long or something (proof done by a computer ) ? I mean how can you even be sure that it is correct ? There might be some error somewhere.
cll7793@lemmy.world 10 months ago
Thanks for the comment! It is cool also pretty aesthetically pleasing!
Image
Reliant1087@lemmy.world 10 months ago
Your map made me think how interesting US would be if there were 4 major political parties. Maybe no one will win the presidential election 🤔